Properties

Label 2.19.ak_cg
Base Field $\F_{19}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $1 - 10 x + 58 x^{2} - 190 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.188320984213$, $\pm0.397309458316$
Angle rank:  $2$ (numerical)
Number field:  4.0.40400.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 220 136400 48230380 17024902400 6130937675500 2213677016632400 799076884811842780 288445071112603750400 104127053138857561322620 37589914862343173855250000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 378 7030 130638 2476050 47053578 893950270 16983778398 322686776890 6131056700698

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.